I have a question similar to another question I've asked here, but it's with more parameters. The question is, need to find the mathematical model for the relationship between number of columns and all possible number of combinations when including three elements, one is not repeating and the two others repeat from one to all columns, below an example of columns equals to 4: suppose that I have the matrix as below:
y = [x r z 0;
x r 0 z;
x r z z;
x z r 0;
x z 0 r;
x z r r;
r x z 0;
r x 0 z;
x r z z; ......etc],
we should have 24 possible combinations.
It means that I have three elements, each column must contain all the three elements. one of those elements 'x' is not increasing, and the others which are 'r' are z are either one or more. my question what's the mathematical model which specify the number of possible combination? For example, for the above matrix, we have four columns, and the possible permutation is 24. what's the relationship between 24and 4 columns? suppose also we have 3 columns or 5 columns, can we calculate the possible number of permutation using such mathematical model?
Thank you